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A309011 Lexicographically earliest sequence of nonnegative integers such that for any n > 0, the palindromic word (a(n), a(n-1), ..., a(1), a(0), a(1), ..., a(n-1), a(n)) is squarefree. 2

%I

%S 0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,3,0,1,0,2,0,1,0,3,0,1,0,

%T 2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,3,0,1,0,2,0,1,0,3,0,1,0,

%U 2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2

%N Lexicographically earliest sequence of nonnegative integers such that for any n > 0, the palindromic word (a(n), a(n-1), ..., a(1), a(0), a(1), ..., a(n-1), a(n)) is squarefree.

%C A word is squarefree if it has no subsequence of the form XX.

%C This sequence has similarities with A007814, the lexicographically earliest squarefree sequence of nonnegative integers.

%C Is this sequence unbounded?

%H Rémy Sigrist, <a href="/A309011/a309011.txt">C program for A309011</a>

%e For n = 0:

%e - a(0) = 0.

%e For n = 1:

%e - "000" is not squarefree,

%e - "101" is squarefree,

%e - hence a(1) = 1,

%e For n = 2:

%e - "01010" is not squarefree,

%e - "11011" is not squarefree,

%e - "21012" is squarefree,

%e - hence a(2) = 2,

%e For n = 3:

%e - "0210120" is squarefree,

%e - hence a(3) = 0.

%o (C) See Links section.

%Y Cf. A007814.

%K nonn

%O 0,3

%A _Rémy Sigrist_, Jul 06 2019

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Last modified January 20 15:35 EST 2022. Contains 350472 sequences. (Running on oeis4.)